Math Problem Statement

Find the square root of 3250

Solution

To find the square root of 3250, we can proceed by breaking it down into its prime factors and simplifying it.

Step-by-step Solution:

  1. Prime Factorization of 3250: 3250=2×53×133250 = 2 \times 5^3 \times 13

  2. Simplifying the Square Root: 3250=2×53×13\sqrt{3250} = \sqrt{2 \times 5^3 \times 13}

    Since we have 52=255^2 = 25 inside the square root, we can take it out:

    3250=5×2×5×13\sqrt{3250} = 5 \times \sqrt{2 \times 5 \times 13}

    Simplifying further:

    3250=5×130\sqrt{3250} = 5 \times \sqrt{130}

  3. Calculating the Approximate Value:

    We can use a calculator to find the approximate square root of 130:

    13011.4\sqrt{130} \approx 11.4

    Therefore,

    32505×11.4=57\sqrt{3250} \approx 5 \times 11.4 = 57

Conclusion:

325057\sqrt{3250} \approx 57

Would you like more details, or do you have any questions?

Related Questions:

  1. How do you simplify square roots involving prime factorization?
  2. What are the properties of square roots for multiplication and division?
  3. How do you approximate square roots without a calculator?
  4. What is the square root of a non-perfect square?
  5. How do you solve quadratic equations involving square roots?

Tip:

To simplify square roots, look for perfect square factors that you can take out of the square root!

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Math Problem Analysis

Mathematical Concepts

Square Roots
Prime Factorization
Simplification

Formulas

Square root formula: √(a × b) = √a × √b

Theorems

Properties of Square Roots
Prime Factorization Theorem

Suitable Grade Level

Grades 8-10